Report Number: CS-TR-70-165
Institution: Stanford University, Department of Computer Science
Title: The scheduling of n tasks with m operations on two processors
Author: Bauer, Henry R.
Author: Stone, Harold S.
Date: July 1970
Abstract: The job shop problem is one scheduling problem for which no
efficient algorithm exists. That is, no algorithm is known in
which the number of computational steps grow algebraically as
the problem enlarges. This paper presents a discussion of the
problem of scheduling N tasks on two processors when each
task consists of three operations. The operations of each
task must be performed in order and among the processors. We
analyze this problem through four sub-problems. Johnson's
scheduling algorithm is generalized to solve two of these
sub-problems, and functional equation algorithms are used to
solve the remaining two problems. Except for one case, the
algorithms are efficient. The exceptional case has been
labelled the "core" problem and the difficulties are
described.
http://i.stanford.edu/pub/cstr/reports/cs/tr/70/165/CS-TR-70-165.pdf